C172 student pilot reported loss of aircraft control on landing resulted in a runway excursion.

Narrative

I was practicing solo pattern work and working on short field landings. I noticed when I kept progressing with my pattern work; the wind kept getting a little stronger and stronger. I noticed it was harder for me to even climb up to (2;700 ft) 300 ft below TPA (3;000 ft) on the upwind. The winds started out calm; then rose up to 4 knots; then 8 knots. I was coming in for my 15th lap; on runway XXL at ZZZ; and was getting blown to the left of the runway. I tried to get myself back to centerline; while I was still in the air. So I applied right aileron; and right rudder. That ended up jetting me past the runway and to the right of the runway into the gravel. I overcorrected and it all happened very quickly. When I saw where I landed; I instantly panicked and tried to get back to the runway as fast as possible and in doing so; I ended up hitting one taxi light. I was filled with even more panic at that time. I ended up back on XXL runway and was asked by ATC if I could make the right on [taxiway] 1; and I confirmed. Tower asked me 'how many passengers were on board' and replied with ' just myself; one only person on board' I was feeling very disappointed at that time. A few moments later tower told me to 'shut down' and I followed the shut down engine procedures on the checklist; which included turning off the avionics. I patiently waited there inside the aircraft by myself; and saw 3 cars driving towards the aircraft I was in. They ended up crossing XXR runway; so it looked to me that they had authority to the runway somehow; they came out of their vehicles and asked me what happened I explained what happened. They asked me if I was associated with any school in the area; I told them 'yes'. And then they asked 'if I was able to start the engine back up'; I told them 'yes'. They told me that they would meet me at the school and I said 'okay; I will meet you there' ; they started up their cars and I saw one of the trucks had a huge bold 'follow me sign' on the back of it. And all 3 cars crossed XXR; I followed right behind them; and ATC then asked me 'if I had authorization to cross XXR'; I was feeling overwhelmed; flustered; and in a state of shock. Since I was told by tower to shut down and since I heard a woman's voice coming from tower when I was told to shut down; I thought that same woman was the one that physically came out to meet me and told me to meet her at the school since none of the persons that came out from their vehicles identified themselves to me. I told Tower 'that the people that met me out told me to meet them at the school' I feeling even more anxious and panicked even more. I switched to ground to check that if it was okay for me to taxi via 2; 3 and they confirmed it was; so I taxied back to [the] flight school and secured the plane. Then the woman person B identified herself there; and told me was with the county; asked me what happened again; and took a picture of my ID; medical; student pilot certificate. Corrective actions have been taken place making sure I am safe to fly being going out with a safety instructor to verify that I am safe to fly by myself; and able to make better aeronautical decision making skills. Next time; I need to apply go-arounds at any phase of flight from now on.